Radiative muon capture in medium heavy nuclei in a relativistic mean field theory model.

Abstract

Radiative and ordinary muon capture are studied in medium heavy nuclei using a relativistic mean field theory approach. A relativistic Fermi gas model is used to describe the nucleus and the local density approximation, together with realistic density distributions, are used to relate the process in infinite nuclear matter to finite nuclei. A number of density dependent effects not considered in previous nonrelativistic calculations are considered, as, for example, the variation of the effective nucleon mass and of the Fermi momentum with the nuclear density. The photon spectrum and the total experimentally accessible radiative rate (i.e., the part of the spectrum with photon momentum {ital k}{ge}57 MeV) are calculated for a variety of nuclei, along with the ordinary muon capture rate. The aim is to understand the sensitivities to the various components and to assess the reliability of such models for extracting the induced pseudoscalar coupling constant {ital g}{sub {ital P}} from the experimental data. We find that the rates are quite dependent on the various inputs, which suggests that it will be difficult to extract {ital g}{sub {ital P}} and casts some doubt on the validity of previous similar calculations. Some interesting qualitative features emerge from a comparison withmore » recent data, however. The absolute rates are too high, which is consistent with other calculations. However, the model does reproduce rather well the {ital Z} dependence of both relative and absolute radiative rates without requiring any quenching of {ital g}{sub {ital P}} in heavy nuclei. Furthermore the model gives an enhancement in the spectrum near the end point as compared to the uniform density model. Such an enhancement seems to be suggested by the data.« less